This invention relates to a digital demodulator, and more particularly to a digital demodulator which demodulates original baseband signals from phase-modulated signals, removing the carrier signals contained therein, through a digital signal processing; the phase-modulated signals are generated through phase shift keying modulation (PSK) or quadrature amplitude modulation (QAM) by synthesizing a first modulated wave provided by modulating a carrier wave with one part of the original baseband signal and a second modulated wave provided by modulating another carrier wave, which has a .pi./2 phase difference from the above carrier wave, with another part of the original baseband signal.
A previously known dmodulator for digitally demodulating signals which are quadrature modulated through PSK, QAM, or the like is a system of passing input signals through Hilbert filters to provide two carrier wave modulated signals which have .pi./2 phase difference from each other, as disclosed in IEEE, Transaction on Communication, COM-25, 2, (1977) pp 238-250. In this previously known demodulator, the two carrier wave modulated signals are provided by two all-pass filters having a .pi./2 phase difference from each other, and accordingly, in order to perform the conversion thereof into baseband signals (demodulation), it is necessary to prepare the cosine component and the sine component of the local carrier and to perform a multiplying operation. In order to digitally perform these operations, it is necessary to write into a read-only-memory (ROM) digital signals representative of the sampled values provided by individually sampling cosine and sine components of a local carrier which have the same frequency as that of received modulated signals, and to multiply the local carrier successively read out from the ROM with received modulated signals. Therefore, a memory (ROM) having the storage capacity of the number of samples corresponding to the sampling frequency, and a multiplying circuit having a high speed operation performance must be provided.